Shelly, Susan, and Samantha are all working at an amusement park for the summer. The manager finds out that one of them left the key in the door to the security office. When he asked them who did it, they replied:

Shelly: Samantha did it.
Susan: Shelly did not do it.
Samantha: I didn’t do it.

The manager concluded that Shelly left the key in the security room’s door.

Use an indirect proof to show that the manager was wrong and that Shelly did not leave the key in the security room’s door.

Question

Shelly, Susan, and Samantha are all working at an amusement park for the summer.  The manager finds out that one of them left the key in the door to the security office.  When he asked them who did it, they replied:
 
Shelly: Samantha did it.
Susan: Shelly did not do it.
Samantha:  I didn’t do it.
 
The manager concluded that Shelly left the key in the security room’s door.
 
Use an indirect proof to show that the manager was wrong and that Shelly did not leave the key in the security room’s door.